Question 1001645
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(x - 3) is a factor of f(x) = x4 - 3x3 - 8x + 24. TRUE or FALSE?
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TRUE.


It is TRUE because  x=3  is the root of the polynomial  f(x):   f(3) = 0.   (Check it !).


Use the &nbsp;<U>remainder theorem</U> &nbsp;(see the lesson &nbsp;<A HREF=http://www.algebra.com/algebra/homework/Polynomials-and-rational-expressions/Divisibility-of-polynomial-f%28x%29-by-binomial-x-a.lesson>Divisibility of polynomial f(x) by binomial x-a</A>&nbsp; in this site).


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A rectangular fish tank with a square bottom whose height is half the length of its side contains 4000 cubic inches 

of water. What is the height of the fish tank?
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Let &nbsp;x&nbsp; be the height of the fish tank.

Then its length is &nbsp;L = 2x &nbsp;and its width is &nbsp;W = 2x inches too, &nbsp;according to the condition. 

(I assume that the tank is full, &nbsp;although you didn't mention it).


Hence, &nbsp;the water volume is &nbsp;V = L*W*H = (2x)*(2x)*x = {{{4x^3}}}, &nbsp;and you have an equation 


{{{4x^3}}} = 4000, &nbsp;&nbsp;&nbsp;&nbsp;or


{{{x^3}}} = 1000.


The solution is &nbsp;x = 10 inches.


<U>Answer</U>. &nbsp;The height of the tank is &nbsp;10 inches.